Machine Learning Techniques for Face Analysis

Roberto Valenti

1

,Nicu Sebe

1

,Theo Gevers

1

,and Ira Cohen

2

1

Faculty of Science,University of Amsterdam,The Netherlands

{rvalenti,nicu,gevers@science.uva.nl}

2

HP Labs,USA

{iracohen@hp.com}

In recent years there has been a growing interest in improving all aspects of the in-

teraction between humans and computers with the clear goal of achieving a natural

interaction,similar to the way human-human interaction takes place.The most ex-

pressive way humans display emotions is through facial expressions.Humans detect

and interpret faces and facial expressions in a scene with little or no effort.Still,

development of an automated system that accomplishes this task is rather difcult.

There are several related problems:detection of an image segment as a face,extrac-

tion of the facial expression information,and classication of the expression (e.g.,in

emotion categories).A system that performs these operations accurately and in real

time would be a major step forward in achieving a human-like interaction between

the man and machine.In this chapter,we present several machine learning algo-

rithms applied to face analysis and stress the importance of learning the structure

of Bayesian network classiers when they are applied to face and facial expression

analysis.

1 Introduction

Information systems are ubiquitous in all human endeavors including scientic,med-

ical,military,transportation,and consumer.Individual users use them for learning,

searching for information (including data mining),doing research (including visual

computing),and authoring.Multiple users (groups of users,and groups of groups

of users) use them for communication and collaboration.And either single or mul-

tiple users use them for entertainment.An information system consists of two com-

ponents:Computer (data/knowledge base,and information processing engine),and

humans.It is the intelligent interaction between the two that we are addressing in

this chapter.

Automatic face analysis has attracted increasing interest in the research commu-

nity mainly due to its many useful applications.A system involving such an analy-

sis assumes that the face can be accurately detected and tracked,the facial features

can be precisely identied,and that the facial expressions,if any,can be precisely

2 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

classied and interpreted.For doing this,in the following,we present in detail the

three essential components of our automatic systemfor human-computer interaction:

face detection,facial feature detection,and facial emotion recognition.This chapter

presents our real time facial expression recognition system [10] which uses a fa-

cial features detector and a model based non-rigid face tracking algorithmto extract

motion features that serve as input to a Bayesian network classier used for recog-

nizing the different facial expressions.Parts of this system has been developed in

collaboration with our colleagues from the Beckman Institute,University of Illinois

at Urbana-Champaign,USA.We present here the components of the systemand give

reference to the publications that contain extensive details on the individual compo-

nents [9,40].

2 Background

2.1 Face Detection

Images containing face are essential to intelligent vision-based human-computer in-

teraction.The rapidly expanding research in face processing is based on the premise

that information about user's identity,state,and intend can be extracted fromimages

and that computers can react accordingly,e.g.,by observing a person's facial expres-

sion.Given an arbitrary image,the goal of face detection is to automatically locate a

human face in an image or video,if it is present.Face detection in a general setting is

a challenging problemfor various reasons.The rst set of reasons are inherent:there

are many types of faces,with different colors,texture,sizes,etc.In addition,the face

is a non-rigid object which can change its appearance.The second set of reasons are

environmental:changing lighting,rotations,translations,and scales of the faces in

natural images.

To solve the problem of face detection,two main approaches can be taken.The

rst is a model based approach,where a description of what is a human face is used

for detection.The second is an appearance based approach,where we learn what

faces are directly from their appearance in images.In this work,we focus on the

latter.

There have been numerous appearance based approaches.We list a few from

recent years and refer to the reviews of Yang et al.[46] and Hjelmas and Low[23] for

further details.Rowley et al.[37] used Neural networks to detect faces in images by

training froma corpus of face and non-face images.Colmenarez and Huang [11] used

maximumentropic discrimination between faces and non-faces to performmaximum

likelihood classication,which was used for a real time face tracking system.Yang

et al.[47] used SNoWbased classiers to learn the face and non-face discrimination

boundary on natural face images.Wang et al.[44] learned a minimum spanning

weighted tree for learning pairwise dependencies graphs of facial pixels,followed by

a discriminant projection to reduce complexity.Viola and Jones [43] used boosting

and a cascade of classiers for face detection.

Machine Learning Techniques for Face Analysis 3

Very relevant to our work is the research of Schneiderman [38] who learns a

sparse structure of statistical dependecies for several object classes including faces.

While analyzing such dependencies can reveal useful information,we go beyond

the scope of Schneiderman's work and present a framework that not only learns the

structure of a face but also allows the use of unlabeled data in classication.

Face detection provides interesting challenges to the underlying pattern classi-

cation and learning techniques.When a raw or ltered image is considered as input

to a pattern classier,the dimension of the space is extremely large (i.e.,the number

of pixels in normalized training images).The classes of face and non-face images

are decidedly characterized by multimodal distribution functions and effective deci-

sion boundaries are likely to be non-linear in the image space.To be effective,the

classiers must be able to extrapolate froma modest number of training samples.

2.2 Facial Feature Detection

Various approaches to facial feature detection exist in the literature.Although many

of the methods have been shown to achieve good results,they mainly focus on nd-

ing the location of some facial features (e.g.,eyes and mouth corners) in restricted

environments (e.g.,constant lighting,simple background,etc.).Since we want to

obtain a complex and accurate system of feature annotation,these methods are not

suitable for us.

In recent years deformable model-based approaches for image interpretation

have been proven very successful,especially in images containing objects with large

variability such as faces.These approaches are more appropriate for our specic case

since they make use of a template (e.g.,the shape of an object).Among the early de-

formable template models is the Active Contour Model by Kass et al.[26] in which

a correlation structure between shape markers is used to constrain local changes.

Cootes et al.[14] proposed a generalized extension,namely Active Shape Models

(ASM),where deformation variability is learned using a training set.Active Appear-

ance Models (AAM) were later proposed in [12] and they are closely related to the

simultaneous formulation of Active Blobs [39] and Morphable Models [24].AAM

can be seen as an extension of ASM which includes the appearance information of

an object.

While active appearance models have been shown to be very successful,they suf-

fer fromimportant drawbacks such as background handling and initialization.Previ-

ous work tried to solve the latter by using an object detector to provide an acceptable

model initialization.In Section 5.2,we bring this concept one step further and we

reduce the existing AAMproblems by considering the initialization information as a

part of the active appearance model.

2.3 Emotion Recognition Research

Ekman and Friesen [17] developed the Facial Action Coding System(FACS) to code

facial expressions where movements on the face are described by a set of action

units (AUs).Each AU has some related muscular basis.This systemof coding facial

4 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

expressions is done manually by following a set of prescribed rules.The inputs are

still images of facial expressions,often at the peak of the expression.This process is

very time-consuming.

Ekman's work inspired many researchers to analyze facial expressions by means

of image and video processing.By tracking facial features and measuring the amount

of facial movement,they attempt to categorize different facial expressions.Recent

work on facial expression analysis and recognition has used these basic expres-

sions or a subset of them.The two recent surveys in the area [35,19] provide an in

depth reviewof many of the research done in automatic facial expression recognition

in recent years.

The work in computer-assisted quantication of facial expressions did not start

until the 1990s.Black and Yacoob [2] used local parameterized models of image

motion to recover non-rigid motion.Once recovered,these parameters were used as

inputs to a rule-based classier to recognize the six basic facial expressions.Essa

and Pentland [18] used an optical ow region-based method to recognize expres-

sions.Oliver et al.[32] used lower face tracking to extract mouth shape features and

used them as inputs to an HMM based facial expression recognition system (rec-

ognizing neutral,happy,sad,and an open mouth).Chen [5] used a suite of static

classiers to recognize facial expressions,reporting on both person-dependent and

person-independent results.Cohen et al.[10] describe classication schemes for fa-

cial expression recognition in two types of settings:dynamic and static classication.

In the static setting,the authors learn the structure of Bayesian networks classiers

using as input 12 motion units given by a face tracking system for each frame in a

video.For the dynamic setting,they used a multi-level HMMclassier that combines

the temporal information and allows not only to performthe classication of a video

segment to the corresponding facial expression,as in the previous works on HMM

based classiers,but also to automatically segment an arbitrary long sequence to the

different expression segments without resorting to heuristic methods of segmenta-

tion.

These methods are similar in that they rst extract some features fromthe images,

then these features are used as inputs into a classication system,and the outcome

is one of the preselected emotion categories.They differ mainly in the features ex-

tracted from the video images and in the classiers used to distinguish between the

different emotions.

3 Learning Classiers for Human-Computer Interaction

Many pattern recognition and human-computer interaction applications require the

design of classiers.Classication is the task of systematic arrangement in groups

or categories according to some set of observations,e.g.,classifying images to those

containing human faces and those that do not or classifying individual pixels as be-

ing skin or non-skin.Classication is a natural part of daily human activity and is

performed on a routine basis.One of the tasks in machine learning has been to give

the computer the ability to perform classication in different problems.In machine

Machine Learning Techniques for Face Analysis 5

classication,a classier is constructed which takes as input a set of observations

(such as images in the face detection problem) and outputs a prediction of the class

label (e.g.,face or no face).The mechanism which performs this operation is the

classier.

We are interested in probabilistic classiers,in which the observations and class

are treated as randomvariables,and a classication rule is derived using probabilistic

arguments (e.g.,if the probability of an image being a face given that we observed

two eyes,nose,and mouth in the image is higher than some threshold,classify the

image as a face).We consider two aspects.First,most of the research mentioned

in the previous section tried to classify each observable independent from each the

others.We want to take a different approach:can we learn the dependencies (the

structure) between the observables (e.g.,the pixels in an image patch)?Can we use

this structure for classication?To achieve this we use Bayesian Networks.Bayesian

Networks can represent joint distributions in an intuitive and efcient way;as such,

Bayesian Networks are naturally suited for classication.Second,we are interested

in using a framework that allows for the usage of labeled and unlabeled data (also

called semi-supervised learning).The motivation for semi-supervised learning stems

fromthe fact that labeled data are typically much harder to obtain compared to unla-

beled data.For example,in facial expression recognition it is easy to collect videos

of people displaying emotions,but it is very tedious and difcult to label the video

to the corresponding expressions.Bayesian Networks are very well suited for this

task:they can be learned with labeled and unlabeled data using maximumlikelihood

estimation.

Is there value to unlabeled data in supervised learning of classiers?This fun-

damental question has been increasingly discussed in recent years,with a general

optimistic viewthat unlabeled data hold great value.Due to an increasing number of

applications and algorithms that successfully use unlabeled data [31,41,1] and mag-

nied by theoretical issues over the value of unlabeled data in certain cases [4,33],

semi-supervised learning is seen optimistically as a learning paradigm that can re-

lieve the practitioner from the need to collect many expensive labeled training data.

However,several disparate empirical evidences in the literature suggest that there are

situations in which the addition of unlabeled data to a pool of labeled data,causes

degradation of the classier's performance [31,41,1],in contrast to improvement of

performance when adding more labeled data.Intrigued by these discrepancies,we

performed extensive experiments,reported in [9].Our experiments suggested that

performance degradation can occur when the assumed classier's model is incorrect.

Such situations are quite common,as one rarely knows whether the assumed model

is an accurate description of the underlying true data generating distribution.More

details are given below (for the sake of consistency we keep the same notations as

the one introduced in [9]).

The goal is to classify an incoming vector of observables X.Each instantiation

of X is a sample.There exists a class variable C;the values of C are the classes.

Let P(C,X) be the true joint distribution of the class and features fromwhich any a

sample of some (or all) of the variables fromthe set {C,X} is drawn,and let p(C,X)

6 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

be the density distribution associated with it.We want to build classiers that receive

a sample x and output either one of the values of C.

Probabilities of (C,X) are estimated fromdata and then are fed into the optimal

classication rule.Also,a parametrical model p(C,X|θ) is adopted.An estimate of

θ is denoted by

ˆ

θ and we denote throughout by

ˆ

θ

∗

the assimptotic value of

ˆ

θ.If the

distribution p(C,X) belongs to the family p(C,X|θ),we say the model is correct;

otherwise,we say the model is incorrect.We use estimation bias loosely to mean

the expected difference between p(C,X) and the estimated p

C,X|

ˆ

θ

.

The analysis presented in [9] and summarized here is based on the work of

White [45] on the properties of maximum likelihood estimators without assum-

ing model correctness.White [45] showed that under suitable regularity condi-

tions,maximum likelihood estimators converge to a parameter set θ

∗

that mini-

mizes the Kullback-Leibler (KL) distance between the assumed family of distri-

butions,p(Y |θ),and the true distribution,p(Y ).White [45] also shows that the

estimator is asymptotically Normal,i.e.,

√N(

ˆ

θ

N

− θ

∗

) ∼ N(0,C

Y

(θ)) as N

(the number of samples) goes to innity.C

Y

(θ) is a covariance matrix equal to

A

Y

(θ)

−1

B

Y

(θ)A

Y

(θ)

−1

,evaluated at θ

∗

,where A

Y

(θ) and B

Y

(θ) are matrices

whose (i,j)'th element ( i,j = 1,...,d,where d is the number of parameters) is

given by:

A

Y

(θ) = E

∂

2

log p(Y |θ)/∂θ

i

θ

j

,

B

Y

(θ) = E[(∂ log p(Y |θ)/∂θ

i

)(∂ log p(Y |θ)/∂θ

j

)].

Using these denitions,in [9] the following theoremwas introduced:

Theorem1.Consider supervised learning where samples are randomly labeled with

probability λ.Adopt the regularity conditions in Theorems 3.1,3.2,3.3 from [45],

with Y replaced by (C,X) and by X,and also assume identiability for the marginal

distributions of X.Then the value of θ

∗

,the limiting value of maximum likelihood

estimates,is:

arg max

θ

(λE[log p(C,X|θ)] +(1 −λ)E[log p(X|θ)]),(1)

where the expectations are with respect to p(C,X).Additionally,

√N(

ˆ

θ

N

−θ

∗

) ∼

N(0,C

λ

(θ)) as N →∞,where C

λ

(θ) is given by:

C

λ

(θ) = A

λ

(θ)

−1

B

λ

(θ)A

λ

(θ)

−1

with,(2)

A

λ

(θ) =

λA

(C,X)

(θ) +(1 −λ)A

X

(θ)

and

B

λ

(θ) =

λB

(C,X)

(θ) +(1 −λ)B

X

(θ)

,

evaluated at θ

∗

.✷

For a proof of this theoremwe direct the interested reader to [9].Here we restrict

only to a few observations.Expression (1) indicates that semi-supervised learning

can be viewed asymptotically as a convex combination of supervised and unsu-

pervised learning.As such,the objective function for semi-supervised learning is a

Machine Learning Techniques for Face Analysis 7

combination of the objective function for supervised learning (E[log p(C,X|θ)]) and

the objective function for unsupervised learning (E[log p(X|θ)]).

Denote by θ

∗

λ

the value of θ that maximizes Expression (1) for a given λ.Then,

θ

∗

1

is the asymptotic estimate of θ for supervised learning,denoted by θ

∗

l

.Likewise,

θ

∗

0

is the asymptotic estimate of θ for unsupervised learning,denoted by θ

∗

u

.

The asymptotic covariance matrix is positive denite as B

Y

(θ) is positive de-

nite,A

Y

(θ) is symmetric for any Y,and

θA(θ)

−1

B

Y

(θ)A(θ)

−1

θ

T

= w(θ)B

Y

(θ)w(θ)

T

> 0,

where w(θ) = θA

Y

(θ)

−1

.We see that asymptotically,an increase in N,the number

of labeled and unlabeled samples,will lead to a reduction in the variance of

ˆ

θ.Such a

guarantee can perhaps be the basis for the optimistic viewthat unlabeled data should

always be used to improve classication accuracy.In [9] it was shown that this ob-

servation holds when the model is correct,and that when the model is incorrect this

observation might not always hold.

3.1 Model Is Correct

Suppose rst that the family of distributions P(C,X|θ) contains the distribution

P(C,X);that is,P(C,X|θ

) = P(C,X) for some θ

.Under this condition,the

maximum likelihood estimator is consistent,thus,θ

∗

l

= θ

∗

u

= θ

given identiabil-

ity.Thus,θ

∗

λ

= θ

for any 0 ≤ λ ≤ 1.

Additionally,using White's results [45],A(θ

∗

λ

) = −B(θ

∗

λ

) = I(θ

∗

λ

),where I()

denotes the Fisher information matrix.Thus,the Fisher information matrix can be

written as:

I(θ) = λI

l

(θ) +(1 −λ)I

u

(θ),(3)

which matches the derivations made by Zhang and Oles [48].The signicance of

Expression (3) is that it allows the use of the Cramer-Rao lower bound (CRLB) on

the covariance of a consistent estimator:

Cov(

ˆ

θ

N

) ≥

1N

(I(θ))

−1

(4)

where N is the number of data (both labeled and unlabeled) and Cov(

ˆ

θ

N

) is the

estimator's covariance matrix with N samples.

Consider the Taylor expansion of the classication error around θ

,as suggested

by Shahshahani and Landgrebe [41],linking the decrease in variance associated with

unlabeled data to a decrease in classication error,and assume the existence of nec-

essary derivatives:

e(

ˆ

θ) ≈ e

B

+

∂e(θ) ∂θ

θ

ˆ

θ −θ

+

12

tr

∂

2

e(θ)∂θ

2

θ

ˆ

θ −θ

ˆ

θ −θ

T

.(5)

8 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

Take expected values on both sides.Asymptotically the expected value of the

second term in the expansion is zero,as maximumlikelihood estimators are asymp-

totically unbiased when the model is correct.Shahshahani and Landgrebe [41] thus

argue that

E

e(

ˆ

θ)

≈ e

B

+(1/2)tr

(∂

2

e(θ)/∂θ

2

)|

θ

Cov(

ˆ

θ)

where e

B

= e(θ

) is the Bayes error rate.They also showthat if Cov(θ

) ≥ Cov(θ

)

for some θ

and θ

,then the second term in the approximation is larger for θ

than

for θ

.Because I

u

(θ) is always positive denite,I

l

(θ) ≤ I(θ).Thus,using the

Cramer-Rao lower bound (Expression (4)) the covariance with labeled and unlabeled

data is smaller than the covariance with just labeled data,leading to the conclusion

that unlabeled data must cause a reduction in classication error when the model is

correct.It should be noted that this argument holds as the number of records goes to

innity,and is an approximation for nite values.

3.2 Model Is Incorrect

A more realistic scenario desribed in detail in [9] is when the distribution P(C,X)

does not belong to the family of distributions P(C,X|θ).In view of Theorem 1,it

is clear that unlabeled data can have the deleterious effect observed occasionally in

the literature.Suppose that θ

∗

u

= θ

∗

l

and that e(θ

∗

u

) > e(θ

∗

l

) (for the difculties in

estimating e(θ

∗

u

) and a solution for this please see [9]).If a large number of labeled

samples is observed,the classication error is approximated by e(θ

∗

l

).If we then

have more samples,most of which unlabeled,we eventually reach a point where the

classication error approaches e(θ

∗

u

).So,the net result is that we started with clas-

sication error close to e(θ

∗

l

),and by adding a large number of unlabeled samples,

classication performance degraded (see again [9] for more details).The basic fact

here is that estimation and classication bias are affected differently by different val-

ues of λ.Hence,a necessary condition for this kind of performance degradation is

that e(θ

∗

u

) = e(θ

∗

l

);a sufcient condition is that e(θ

∗

u

) > e(θ

∗

l

).

The focus on asymptotics is adequate as we want to eliminate phenomena that

can vary from dataset to dataset.If e(θ

∗

l

) is smaller than e(θ

∗

u

),then a large enough

labeled dataset can be dwarfed by a much larger unlabeled dataset the classica-

tion error using the whole dataset can be larger than the classication error using the

labeled data only.

3.3 Discussion

Despite the shortcomings of semi-supervised learning presented in the previous sec-

tions,we do not discourage its use.Understanding the causes of performance degra-

dation with unlabeled data motivates the exploration of new methods attempting

to use positively the available unlabeled data.Incorrect modeling assumptions in

Bayesian networks culminate mainly as discrepancies in the graph structure,sig-

nifying incorrect independence assumptions among variables.To eliminate the in-

creased bias caused by the addition of unlabeled data we can try simple solutions,

Machine Learning Techniques for Face Analysis 9

such as model switching (Section 4.2) or attempt to learn better structures.We de-

scribe likelihood based structure learning methods (Section 4.3) and a possible alter-

native:classication driven structure learning (Section 4.4).In cases where relatively

mild changes in structure still suffer from performance degradation from unlabeled

data,there are different approaches that can be taken:discard the unlabeled data,give

thema different weight (Section 4.5),or use the alternative of actively labeling some

of the unlabeled data (Section 4.6).

To summarize,the main conclusions that can be derived fromour analysis are:

• Labeled and unlabeled data contribute to a reduction in variance in semi-supervised

learning under maximumlikelihood estimation.This is true regardless of whether

the model is correct or not.

• If the model is correct,the maximum likelihood estimator is unbiased and both

labeled and unlabeled data contribute to a reduction in classication error by

reducing variance.

• If the model is incorrect,there may be different asymptotic estimation biases

for different values of λ (the ratio between the number of labeled and unlabeled

data).Asymptotic classication error may also be different for different values

of λ.An increase in the number of unlabeled samples may lead to a larger bias

fromthe true distribution and a larger classication error.

In the next section,we discuss several possible solutions for the problem of perfor-

mance degradation in the framework of Bayesian network classiers.

4 Learning the Structure of Bayesian Network Classiers

The conclusion of the previous section indicates the importance of obtaining the cor-

rect structure when using unlabeled data in learning a classier.If the correct struc-

ture is obtained,unlabeled data improve the classier;otherwise,unlabeled data can

actually degrade performance.Somewhat surprisingly,the option of searching for

better structures was not proposed by researchers that previously witnessed the per-

formance degradation.Apparently,performance degradation was attributed to unpre-

dictable,stochastic disturbances in modeling assumptions,and not to mistakes in the

underlying structure something that can be detected and xed.

4.1 Bayesian Networks

Bayesian Networks [36] are tools for modeling and classication.A Bayesian Net-

work (BN) is composed of a directed acyclic graph in which every node is associated

with a variable X

i

and with a conditional distribution p(X

i

|Π

i

),where Π

i

denotes

the parents of X

i

in the graph.The joint probability distribution is factored to the

collection of conditional probability distributions of each node in the graph as:

p(X

1

,...,X

n

) =

n

i=1

p(X

i

|Π

i

).(6)

10 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

The directed acyclic graph is the structure,and the distributions p(X

i

|Π

i

) represent

the parameters of the network.We say that the assumed structure for a network,

S

,is correct when it is possible to nd a distribution,p(C,X|S

),that matches the

distribution that generates data,p(C,X);otherwise,the structure is incorrect.In the

above notations,Xis an incoming vector of features.The classier receives a record

x and generates a label ˆc(x).An optimal classication rule can be obtained fromthe

exact distribution p(C,X) which represents the a-posteriori probability of the class

given the features.

Maximum likelihood estimation is one of the main methods to learn the param-

eters of the network.When there are missing data in training set,the Expectation

Maximization (EM) algorithm[15] can be used to maximize the likelihood.

As a direct consequence of the analysis in Section 3,a Bayesian network that

has the correct structure and the correct parameters is also optimal for classication

because the a-posteriori distribution of the class variable is accurately represented

(see [9] for a detailed analysis on this issue).As pointed out in [9] and [8] to solve

the problem of performance degradation in BNs,there is a need to carefull analyze

the structure of the BN classier used in the classication.

4.2 Switching between Simple Models

One attempt to overcome the performance degradation fromunlabeled data could be

to switch models as soon as degradation is detected.Suppose that we learn a classi-

er with labeled data only and we observe a degradation in performance when the

classier is learned with labeled and unlabeled data.We can switch to a more com-

plex structure at that point.An interesting idea is to start with a Naive Bayes classier

in which the features are assumed independent given the class.If performance de-

grades with unlabeled data,switch to a different type of Bayesian Network classier,

namely the Tree-Augmented Naive Bayes classier (TAN) [21].

In the TAN classier structure the class node has no parents and each feature

has the class node and at most one other feature as parents,such that the result is

a tree structure for the features.Learning the most likely TAN structure has an ef-

cient and exact solution [21] using a modied Chow-Liu algorithm[7].Learning the

TANclassiers when there are unlabeled data requires a modication of the original

algorithmto what we named the EM-TAN algorithm[10].

If the correct structure can be represented using a TAN structure,this approach

will indeed work.However,even the TANstructure is only a small set of all possible

structures.Moreover,as the examples in the experimental section show,switching

fromNBto TANdoes not guarantee that the performance degradation will not occur.

Very relevant is the research of Baluja [1].The author uses labeled and unlabeled

data in a probabilistic classier framework to detect the orientation of a face.In

his results,he obtained excellent classication results,but there were cases where

unlabeled data degraded performance.As a consequence,he decided to switch from

a Naive Bayes approach to more complex models.Following this intuitive direction,

we explain Baluja's observations and provide a solution to the problem:structure

learning.

Machine Learning Techniques for Face Analysis 11

4.3 Beyond Simple Models

A different approach to overcome performance degradation is to learn the structure

of the Bayesian network without restrictions other than the generative one

3

.There

are a number of such algorithms in the literature (among them [20,3,6]).Nearly

all structure learning algorithms use the`likelihood based'approach.The goal is to

nd structures that best t the data (with perhaps a prior distribution over different

structures).Since more complicated structures have higher likelihood scores,penal-

izing terms are added to avoid overting to the data,e.g,the minimum description

length (MDL) term.The difculty of structure search is the size of the space of pos-

sible structures.With nite amounts of data,algorithms that search through the space

of structures maximizing the likelihood,can lead to poor classiers because the a-

posteriori probability of the class variable could have a small effect on the score [21].

Therefore,a network with a higher score is not necessarily a better classier.Fried-

man et al.[21] suggest changing the scoring function to focus only on the posterior

probability of the class variable,but show that it is not computationally feasible.

The drawbacks of likelihood based structure learning algorithms could be mag-

nied when learning with unlabeled data;the posterior probability of the class has a

smaller effect during the search,while the marginal of the features would dominate.

Therefore,we decided to take a different approach presented in the next section.

4.4 Classication Driven Stochastic Structure Search

As pointed out in [8] one ellegant solution is to nd the structure that minimizes the

probability of classication error directly.To do so the classication driven stochastic

search algorithm (SSS) was proposed in [9].The basic idea of this approach is that,

since one is interested in nding a structure that performs well as a classier,it is

natural to design an algorithm that use classication error as the guide for structure

learning.For completness we summarize the main observation here and we direct

the interested reader to [8] for a complete analysis.

One important observation is that unlabeled data can indicate incorrect struc-

ture through degradation of classication performance.Additionally,we also saw

previously that classication performance improves with the correct structure.As a

consequence,a structure with higher classication accuracy over another indicates

an improvement towards nding the optimal classier.

To learn structure using classication error,it is necessary to adopt a strategy for

efciently searching through the space of all structures while avoiding local maxima.

As there is no simple closed-formexpression that relates structure with classication

error,it is difcult to design a gradient descent algorithmor a similar iterative method

which would be in any case prone to nd local minima due to the size of the search

space.

In [8] the following measure was proposed to be maximized:3

A Bayesian network classier is a generative classier when the class variable is an ances-

tor (e.g.,parent) of some (or all) features.

12 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

Denition 1.The inverse error measure for structure S

is

inv

e

(S

) =

1p

S

(ˆc(X)=C)

S

1p

S

(ˆc(X)=C)

,(7)

where the summation is over the space of possible structures and p

S

(ˆc(X) = C) is

the probability of error of the best classier learned with structure S.

Metropolis-Hastings sampling [30] can be used to generate samples from the

inverse error measure,without the need to compute it for all possible structures.

For constructing the Metropolis-Hastings sampling,a neighborhood of a structure is

dened as the set of directed acyclic graphs to which we can transit in the next step.

Transition is done using a predened set of possible changes to the structure;at each

transition a change consists of a single edge addition,removal,or reversal.In [8] the

acceptance probability of a candidate structure,S

new

,to replace a previous structure,

S

t

is dened as follows:

min

1,

inv

e

(S

new

) inv

e

(S

t

)

1/T

q(S

t

|S

new

)q(S

new

|S

t

)

= min

1,

p

t

errorp

new

error

1/T

N

tN

new

(8)

where q(S

|S) is the transition probability from S to S

and N

t

and N

new

are the

sizes of the neighborhoods of S

t

and S

new

,respectively;this choice corresponds

to equal probability of transition to each member in the neighborhood of a structure.

This choice of neighborhood and transition probability creates a Markov chain which

is aperiodic and irreducible,thus satisfying the Markov chain Monte Carlo (MCMC)

conditions [27].

The parameter T is used as a temperature factor in the acceptance probability.As

such,T close to 1 would allowacceptance of more structures with higher probability

of error than previous structures.T close to 0 mostly allows acceptance of structures

that improve probability of error.A xed T amounts to changing the distribution

being sampled by the MCMC,while a decreasing T is a simulated annealing run,

aimed at nding the maximumof the inverse error measures.The rate of decrease of

the temperature determines the rate of convergence.Asymptotically in the number

of data,a logarithmic decrease of T guarantees convergence to a global maximum

with probability that tends to one [22].

The SSS algorithm,with a logarithmic cooling schedule T,can nd a structure

that is close to minimumprobability of error.The estimate of the classication error

of a given structure is obtained by using the labeled training data.Therefore,to avoid

overtting,a multiplicative penalty termis required.This penalty term,derived from

the Vapnik-Chervonenkis (VC) bound on the empirical classication error,penalizes

complex classiers thus keeping the balance between bias and variance (for more

details we refer the reader to [9]).

Machine Learning Techniques for Face Analysis 13

4.5 Should Unlabeled Be Weighed Differently?

An interesting strategy,suggested by Nigamet al.[31] is to change the weight of the

unlabeled data (reducing their effect on the likelihood).The basic idea in Nigam et

al's estimators is to produce a modied log-likelihood that is of the form:

λ

L

l

(θ) +(1 −λ

)L

u

(θ) (9)

where L

l

(θ) and L

u

(θ) are the likelihoods of the labeled and unlabeled data,re-

spectively.For a sequence of λ

,maximize the modied log-likelihood functions to

obtain

ˆ

θ

λ

(

ˆ

θ denotes an estimate of θ),and choose the best one with respect to cross-

validation or testing.This estimator is simply modifying the ratio of labeled to unla-

beled samples for any xed λ

.Note that this estimator can only make sense under

the assumption that the model is incorrect.Otherwise,both terms in Expression (9)

lead to unbiased estimators of θ.

Our experiments in [8] suggest that there is then no reason to impose different

weights on the data,and much less reason to search for the best weight,when the

differences are solely in the rate of reduction of variance.Presumably,there are a

few labeled samples available and a large number of unlabeled samples;why should

we increase the importance of the labeled samples,giving more weight to a termthat

will contribute more heavily to the variance?

4.6 Active Learning

All the methods presented above consider a passive use of unlabeled data.Adiffer-

ent approach is known as active learning,in which an oracle is queried as to the label

of some of the unlabeled data.Such an approach increases the size of the labeled data

set,reduces the classier's variance,and thus reduces the classication error.There

are different ways to choose which unlabeled data to query.The straightforward ap-

proach is to choose a sample randomly.This approach ensures that the data distribu-

tion p(C,X) is unchanged,a desirable property when estimating generative classi-

ers.However,the random sample approach typically requires many more samples

to achieve the same performance as methods that choose to label data close to the de-

cision boundary.We note that,for generative classiers,the latter approach changes

the data distribution therefore leading to estimation bias.Nevertheless,McCallum

and Nigam[29] used active learning with generative models with success.They pro-

posed to rst actively query some of the labeled data followed by estimation of the

model's parameters with the remainder of the unlabeled data.

We performed extensive experiments in [8].Here we present only the main con-

clusions.With correctly specied generative models and a large pool of unlabeled

data,passive use of the unlabeled data is typically sufcient to achieve good per-

formance.Active learning can help reduce the chances of numerical errors (improve

EM starting point,for example),and help in the estimation of classication error.

With incorrectly specied generative models,active learning is very protable in

quickly reducing the error,while adding the remainder of unlabeled data might not

be desirable.

14 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

4.7 Summary

The idea of structure search is particularly promising when unlabeled data are

present.It seems that simple heuristic methods,such as the solution proposed by

Nigamet al.[31] of weighing down the unlabeled data,are not the best strategies for

unlabeled data.We suggest that structure search,and in particular stochastic struc-

ture search,holds the most promise for handling large amount of unlabeled data and

relatively scarce labeled data for classication.We also believe that the success of

structure search methods for classication increases signicantly the breadth of ap-

plications of Bayesian networks.

In a nutshell,when faced with the option of learning with labeled and unlabeled

data,our discussion suggests following the following path.Start with Naive Bayes

and TANclassiers,learn with only labeled data and test whether the model is correct

by learning with the unlabeled data,using EM and EM-TAN.If the result is not

satisfactory,then SSS can be used to attempt to further improve performance with

enough computational resources.If none of the methods using the unlabeled data

improve performance over the supervised TAN(or Naive Bayes),active learning can

be used,as long as there are resources to label some samples.

5 Experiments

For the experiments,we used our real time facial expression recognition system[10].

This is composed of a face detector which is used as an input to a facial feature de-

tection module.Using the extracted facial features,a face tracking algorithmoutputs

a vector of motion features of certain regions of the face.The features are used as

inputs to a Bayesian network classier.

The face tracking we use in our system is based on a system developed by Tao

and Huang [42] called the piecewise B´ezier volume deformation (PBVD) tracker.

The face tracker uses a model-based approach where an explicit 3Dwireframe model

of the face is constructed.A generic face model is then warped to t the detected

facial features.The face model consists of 16 surface patches embedded in B

´

ezier

volumes.The surface patches dened in this way are guaranteed to be continuous

and smooth.The shape of the mesh can be changed by changing the locations of the

control points in the B´ezier volume.Asnap shot of the system,with the face tracking

and the corresponding recognition result is shown in Figure 1.

In Section 5.1,we start by investigating the use Bayesian network classiers

learned with labeled and unlabeled data for face detection.We present our results

on two standard databases and show good results even if we use a very small set

of labeled data.Subsequently,in Section 5.2,we present our facial feature detection

module which uses the input given from the face detector and outputs the location

of relevant facial features.Finally,in Section 5.3,we discuss the facial expression

recognition results obtained by incorporating the facial feature detected inside the

PBVD tracker.

Machine Learning Techniques for Face Analysis 15Fig.1.A snap shot of our realtime facial expression recognition system.On the left side is a

wireframe model overlayed on a face being tracked.On the right side the correct expression,

Happy,is detected (the bars show the relative probability of Happy compared to the other

expressions).The subject shown is fromthe Cohn-Kanade database.

5.1 Face Detection Experiments

In our face detection experiments we propose to use Bayesian network classiers,

with the image pixels of a predened window size as the features in the Bayesian

network.Among the different works,those of Colmenarez and Huang [11] and Wang

et al.[44] are more related to the Bayesian network classication methods for face

detection.Both learn some`structure'between the facial pixels and combine themto

a probabilistic classication rule.Both use the entropy between the different pixels

to learn pairwise dependencies.

Our approach in detecting faces is an appearance based approach,where the in-

tensity of image pixels serve as the features for the classier.In a natural image,

faces can appear at different scales,rotations,and location.For learning and dening

the Bayesian network classiers,we must look at xed size windows and learn how

a face appears in such windows,where we assume that the face appears in most of

the window's pixels.

The goal of the classier is to determine if the pixels in a xed size window

are those of a face or non-face.While faces are a well dened concept,and have

a relatively regular appearance,it is harder to characterize non-faces.We therefore

model the pixel intensities as discrete randomvariables,as it would be impossible to

dene a parametric probability distribution function (pdf) for non-face images.For

8-bit representation of pixel intensity,each pixel has 256 values.Clearly,if all these

values are used for the classier,the number of parameters of the joint distribution

is too large for learning dependencies between the pixels (as is the case of TANclas-

siers).Therefore,there is a need to reduce the number of values representing pixel

intensity.Colmenarez and Huang [11] used 4 values per pixel using xed and equal

bin sizes.We use non-uniform discretization using the class conditional entropy as

16 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

the mean to bin the 256 values to a smaller number.We use the MLC++ software for

that purpose as is described in [16].

Note that our methodology can be extended to other face detection methods

which use different features.The complexity of our method is O(n),where n is

the number of features (pixels in our case) considered in each image window.

We test the different approaches described in Section 4,with both labeled and

unlabeled data.For training the classier we used a dataset consisting of 2,429 faces

and 10,000 non-faces obtained fromthe MIT CBCL Face database#1

4

.Examples of

face images fromthe database are presented in Figure 2.Each face image is cropped

and resampled to a 19 × 19 window,thus we have a classier with 361 features.

We also randomly rotate and translate the face images to create a training set of

10,000 face images.In addition we have available 10,000 non-face images.We leave

out 1,000 images (faces and non-faces) for testing and train the Bayesian network

classiers on the remaining 19,000.In all the experiments we learn a Naive Bayes,

TAN,and a general generative Bayesian network classier,the latter using the SSS

algorithm.Fig.2.Randomly selected face examples.

In Table 1 we summarize the results obtained for different algorithms and in the

presence of increasing number of unlabeled data.We xed the false alarm to 1%,

5%,and 10%and we computed the detection rates.We rst learn using all the train-

ing data being labeled (that is 19,000 labeled images).The classier learned with

the SSS algorithm outperforms both TAN and NB classiers,and all perform quite

well,achieving high detection rates with a low rate of false alarm.Next we remove

the labels of some of the training data and train the classiers.In the rst case,we

remove the labels of 97.5% of the training data (leaving only 475 labeled images).4

http://www.ai.mit.edu/projects/cbcl

Machine Learning Techniques for Face Analysis 17

Table 1.Detection rates (%) for various numbers of false positives

Detector

False positives1%5%10%19,000 labeled74.3189.2192.72475 labeled68.3786.5589.45475 labeled + 18,525 unlabeled66.0585.7386.98250 labeled65.5984.1387.67NB250 labeled + 18,750 unlabeled65.1583.8186.0719,000 labeled91.8296.4299.11475 labeled86.5990.8494.67475 labeled + 18,525 unlabeled85.7790.8794.21250 labeled75.3787.9792.56TAN250 labeled + 18,750 unlabeled77.1989.0891.4219,000 labeled90.2798.2699.87475 labeled + 18,525 unlabeled88.6696.8998.77SSS250 labeled + 18,750 unlabeled86.6495.2997.9319,000 labeled87.7893.8494.14475 labeled82.6189.6691.12SVM250 labeled77.6487.1789.16We see that the NB classier using both labeled and unlabeled data performs very

poorly.The TAN based only on the 475 labeled images and the TAN based on the

labeled and unlabeled images are close in performance,thus there was no signicant

degradation of performance when adding the unlabeled data.When only 250 labeled

data are used (the labels of about 98.7%of the training data were removed),NB with

both labeled and unlabeled data performs poorly,while SSS outperforms the other

classiers with no great reduction of performance compared to the previous cases.

For benchmarking,we also implemented a SVMclassier (we used the implemen-

tation of Osuna et al.[34]).Note that this classier starts off very good,but does not

improve performance.

In summary,note that the detection rates for NB are lower than the ones obtained

for the other detectors.Overall,the results obtained with SSS are the best.We see

that even in the most difcult cases,there was sufcient amount of unlabeled data to

achieve almost the same performance as with a large sized labeled dataset.

We also tested our system on the CMU test set [37] consisting of 130 images

with a total of 507 frontal faces.The results are summarized in Table 2.Note that

we obtained comparable results with the results obtained by Viola and Jones [43]

and better than the results of Rowley et al.[37].Examples of the detection results on

some of the images of the CMU test are presented in Figure 3.We noticed similar

failure modes as Viola and Jones [43].Since,the face detector was trained only on

frontal faces our system failes to detect faces if they have a signicant rotation out

of the plane (toward a prole view).The detector has also problems with the images

in which the faces appear dark and the background is relatively light.Inevitably,we

also detect false positive especially in some texture regions.

18 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira CohenFig.3.Output of the systemon some images of the CMU test using the SSS classier learned

with 19,000 labeled data.MFs represents the number of missed faces and FDs is the number

of false detections.

5.2 Facial Feature Detection

In this section,we introduce a novel way to unify the knowledge of a face detector

inside an active appearance model [12],using what we call a'virtual structuring

element',which limits the possible settings of the AAM in an appearance-driven

Machine Learning Techniques for Face Analysis 19

Table 2.Detection rates (%) for various numbers of false positives on the CMU test set.

Detector

False positives10%20%19,000 labeled91.792.84475 labeled + 18,525 unlabeled89.6791.03SSS250 labeled + 18,750 unlabeled86.6489.17Viola-Jones [43]92.193.2Rowley et al.[37]-89.2manner.We propose this visual artifact as a good solution for the background linking

problems and respective generalization problems of basic AAMs.

The main idea of using an AAM approach is to learn the possible variations

of facial features exclusively on a probabilistic and statistical basis of the existing

observations (i.e.,which relation holds in all the previously seen instances of facial

features).This can be dened as a combination of shapes and appearances.

At the basis of AAM search is the idea to treat the tting procedure of a com-

bined shape-appearance model as an optimization problemin trying to minimize the

difference vector between the image I and the generated model M of shape and

appearance:δI = I −M.

Cootes et al.[12] observed that each search corresponds to a similar class of

problems where the initial and the nal model parameters are the same.This class can

be learned ofine (when we create the model) saving high-dimensional computations

during the search phase.

Learning the class of problems means that we have to assume a relation R be-

tween the current error image δI and the needed adjustments in the model parame-

ters m.The common assumption is to use a linear relation:δm = RδI.Despite the

fact that more accurate models were proposed [28],the assumption of linearity was

shown to be sufciently accurate to obtain good results.To nd Rwe can conduct a

series of experiments on the training set,where the optimal parameters mare known.

Each experiment consists of displacing a set of parameters by a know amount and in

measuring the difference between the generated model and the image under it.Note

that when we displace the model fromits optimal position and we calculate the error

image δI,the image will surely contain parts of the background.

What remains to discuss is an iterative optimization procedure that uses the found

predictions.The rst step is to initialize the mean model in an initial position and

the parameters within the reach of the parameter prediction range (which depends

on the perturbation used during training).Iteratively,a sample of the image under

the initialization is taken and compared with the model instance.The differences

between the two appearances are used to predict the set of parameters that would

perhaps improve the similarity.In case a prediction fails to improve the similarity,it

is possible to damp or amplify the prediction several times and maintain the one with

the best result.For an overview of some possible variations to the original AAMs

20 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

algorithm refer to [13].An example of the AAMsearch is shown in Fig.4 where a

model is tted to a previously unseen face.(a) Unseen face (b) Initialization (c) Converged model

Fig.4.Results of an AAMsearch on an unseen face

One of the main drawbacks of the AAMis coming from its very basic concept:

when the algorithm learns how to solve the optimization ofine,the perturbation

applied to the model inevitably takes parts of the background into account.This

means that instead of learning how to generally solve the class of problems,the al-

gorithmactually learns howto solve it only for the same or similar background.This

makes AMMs domain-specic,that is,the AAMtrained for a shape in a predened

environment has difculties when used on the same shape immersed in a different

environment.Since we always need to perturbate the model and to take into account

the background,an often used idea is to constrain the shape deformation within pre-

dened boundaries.Note that a shape constraint does not adjust the deformation,but

will only limit it when it is found to be invalid.

To overcome these deciencies of AAMs,we propose a novel method to vi-

sually integrate the information obtained by a face detector inside the AAM.This

method is based on the observation that an object with a specic and recognizable

feature would ease the successful alignment of its model.As the face detector we

can choose between the one proposed by Viola and Jones [43] and the one presented

in Section 5.1.

Since faces have many highly relevant features,erroneously located ones could

lead the optimization process to converge to local minima.The novel idea is to add a

virtual artifact in each of the appearances in the training and the test sets,that would

inherently prohibit some deformations.We call this artifact a virtual structuring

element (or VSE) since it adds structure in the data that was not available otherwise.

In our specic case,this element adds visual information about the position of the

face.If we assume that the face detector successfully detects a face,we can use that

information to build this artifact.

After experimenting with different VSEs,we propose the following guideline to

choose a good VSE.We should choose a VSE that:(1) Is big enough to steer the

optimization process;(2) Does not create additional uncertainty by covering relevant

features (e.g.,the eyes or nose);(3) Scales accordingly to the dimension of the de-

Machine Learning Techniques for Face Analysis 21

tected face;and (4) Completely or partially removes the high variance areas in the

model (e.g.,background) with uniformones.Fig.5.The effect of a virtual structuring element to the annotation,appearance,and variance

(white indicates a larger variance)

In the used VSE,a black frame with width equal to 20%of the size of the detected

face is built around the face itself.Besides the regular markers that capture the facial

features (see Fig.5 and [10] for details) four newmarkers are added in the corners to

stretch the convex hull of the shape to take in consideration the structuring element.

Around each of those four points,a black circle with the radius of one third of the

size of the face is added.The resulting annotation,shape,and appearance variance

are displayed in Fig.5.Note that in the variance map the initialization variance of

the face detector is automatically included in the model (i.e.,the thick white border

delimitating the VSE).

This virtual structuring element visually passes information between the face

detection and the AAM.We showin the experiments that VSE helps the basic AAMs

in the model generalization and tting performances.

Two datasets were used during the evaluation:(1) a part of the Cohn-Kanade [25]

dataset consisting of 53 male and female subjects,showing neutral frontal faces in a

controlled environment;(2) the Unilever dataset consinsting of 50 females,showing

natural poses in an outdoor uncontrolled environment.The idea is to investigate the

inuence of the VSE when the background is unchanged (Cohn-Kanade) and when

more difcult conditions are present (Unilever).

We evaluate two specic annotations,one named`relevant'(Fig.6(a)) describ-

ing the facial features that are relevant for the facial expression classiers including

the face contours that are needed for face tracking,and the other one named`in-

side'(Fig.6(b)) describing the facial features without the face contours.Note that

the`inside'model is surrounded only by face area (so not by not by background)

so its variance is lower and the model is more robust.To assess the performance of

the AAMwe initialize the mean model (i.e.,the mean shape with the mean appear-

ance) shifted in the Cartesian plane with a predened amount.This simulates some

extremes in the initialization error obtained by the face detector.

22 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen(a) Relevant (b) Inside

Fig.6.The annotations and their respective variance maps over the datasets

The common approach to assess performance of AAMis to compare the results

to a ground truth (i.e.,the annotations in the training set).The following measures are

used:Point to Point Error is the Euclidean distance between each point of the true

shape and the corresponding tted shape;Point to Curve Error is the Euclidean dis-

tance between a tted shape point and the closest point on the linear spline obtained

fromthe true shape points;and Mahalanobis Distance dened as:

D

2

=

t

i=1

m

2

iλ

i

(10)

where m

i

represents the AAMparameters and λ

i

their respective principal compo-

nents.

We perform two types of experiments.In the person independent case we per-

form a leave-one-out cross validation.For the second experiment,the Generalized

AAM test,we merge the two datasets and we create a model which includes all

the different lighting conditions,backgrounds,subject features,and annotations (to-

gether with their respective errors).The goal of this experiment is to test whether the

generalization problems of AAMs could be solved just by using a greater amount of

training data.Cohn-KanadeUnileverPoint-PointPoint-CurveMahalanobisPoint-PointPoint-CurveMahalanobisRelev.16.72 (5.53)9.09 (3.36)47.93 (4.90)54.84 (10.58)29.82 (6.22)79.41 (6.66)Relev.VSE6.73 (0.21)4.34 (0.15)26.46 (1.57)10.14 (2.07)6.53 (1.30)24.75 (3.57)Inside9.53 (3.48)6.19 (2.47)39.55 (3.66)25.98 (7.29)17.69 (5.16)38.20 (4.52)Inside VSE5.85 (0.24)3.76 (0.13)27.14 (1.77)8.99 (1.90)6.37 (1.46)23.45 (2.81)Table 3.Mean and standard error in the person independent test for the two datasets

Table 3 shows the results obtained for the two datasets in the person independent

experiment.Important to notice that the results obtained with Cohn-Kanade datasets

are in most of the cases better than the one obtained with the Unilever dataset.This

Machine Learning Techniques for Face Analysis 23

has to do with the fact that,in the Unilver dataset,the effect of the uncontrolled

lighting condition and background change is more relevant and the model tting is

more difcult.However,in both cases one can see that the use of VSE improved

signicantly the results.Another important aspect is that the use of VSE is more

effective in the case of Unilever database and this is because the VSE is reducing the

background inuence to a larger extend.Interesting to note is that,while the use of

a VSE does not excessively improve the accuracy of the`inside'model,the use of

VSE on the'relevant'model drastically improves its accuracy making it even better

than the basic`inside'model.This result is surprising since in the'relevant'model

parts of the markers are covered by the VSE (i.e.,the forehead and chin markers) we

expected the nal model to inherently generate some errors.Instead,it seems that

the inner parts of the face might steer the outer markers to the optimal position.This

could only mean that there is a proportional relation between the facial countours

and the inside features,which is a very interesting and unexpected property.

In the generalized AAMexperiment (see Table 4),we notice that the results are

generally worse when compared with the person independent results on the`con-

trolled'Cohn-Kanade dataset,but better when compared with the same experiment

on the`uncontrolled'Unilever dataset.Also in this case the VSE implementation

shows very good improvements over the basic AAM implementation.What is im-

portant to note is that the VSE implementation brings the results of the generalized

AAMvery close to the dataset specic results,improving the generalization of basic

AAM.Generalized AAMPoint-PointPoint-CurveMahalanobisRelevant21.05 (0.79)8.45 (0.27)116.22 (3.57)Relevant VSE8.50 (0.20)5.38 (0.12)51.11 (0.91)Inside8.11 (0.21)4.77 (0.10)85.22 (1.98)Inside VSE7.22 (0.17)4.65 (0.09)52.84 (0.96)Table 4.Mean and standard error for Generalized AAM

While the`relevant VSE'model is better than the normal`inside'model,the

`inside VSE'is the model of choice to obtain the best overall results on facial features

detection.In our specic task,we can use the`inside VSE'model to obtain the best

results but we will additionally need some heuristics to correctly position the other

markers which are not included in the model.These missing markers are relevant

for robust face tracking and implicitly for facial expression classication so their

accurate positioning is very important.Since in the case of`inside VSE'model these

markers are not detected explicitly,we indicate the`relevant VSE'model as the best

choice for our purposes.

To better illustrate the effect of using a VSE,Fig.7 shows an example of the

difference in the results when using a`relevant'model and a`relevant VSE'model.

While the rst failed to correctly converge,the second result is optimal for inner

24 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen(a) Relevant (b)Relevant VSE

Fig.7.An example of the difference in the results between a`relevant'and a`relevant VSE'

model

facial features.Empirically,VSE models showed to always overlap to the correct

annotation,avoiding the mistakes generated by unsuccessful alignments like the one

in Fig.7(a).

5.3 Facial Expression Recognition Experiments

As mentioned previously,our systemuses a generic face model consisting of 16 sur-

face patches embedded in B´ezier volumes which is warped to t the detected facial

features.This model is used for tracking the detected facial features.The recovered

motions are represented in terms of magnitudes of some predened motion of the fa-

cial features.Each feature motion corresponds to a simple deformation on the face,

dened in terms of the B ´ezier volume control parameters.We refer to these motions

vectors as motion-units (MU's).Note that they are similar but not equivalent to Ek-

man's AU's [17],and are numeric in nature,representing not only the activation of

a facial region,but also the direction and intensity of the motion.The 12 MU's used

in the face tracker are shown in Figure 8.The MU's are used as the features for the

Bayesian network classiers learned with labeled and unlabeled data.

There are seven categories of facial expressions corresponding to neutral,joy,

surprise,anger,disgust,sad,and fear.For testing we use two databases,in which all

the data is labeled.We removed the labels of most of the training data and learned

the classiers with the different approaches discussed in Section 4.

The rst database was collected by Chen and Huang [5] and is a database of

subjects that were instructed to display facial expressions corresponding to the six

types of emotions.All the tests of the algorithms are performed on a set of ve

people,each one displaying six sequences of each one of the six emotions,starting

and ending at the Neutral expression.The video sampling rate was 30 Hz,and a

typical emotion sequence is about 70 samples long (∼2s).The second database is

the Cohn-Kanade database [25] introduced in the previous section.For each subject

Machine Learning Techniques for Face Analysis 25Fig.8.The facial motion measurements

Table 5.The experimental setup and the classication results for facial expression recogni-

tion with labeled data (L) and labeled + unlabeled data (LUL).Accuracy is shown with the

corresponding 95%condence interval.TrainDataset#lab.#unlab.TestNB-LNB-LULTAN-LTAN-LULSSS-LULChen-Huang30011,9823,55571.25±0.75%58.54±0.81%72.45±0.74%62.87±0.79%74.99±0.71%Cohn-Kanade2002,9801,00072.50±1.40%69.10±1.44%72.90±1.39%69.30±1.44%74.80±1.36%there is at most one sequence per expression with an average of 8 frames for each

expression.

We measure the accuracy with respect to the classication result of each frame,

where each frame in the video sequence was manually labeled to one of the expres-

sions (including Neutral).The results are shown in Table 5,showing classication

accuracy with 95% condence intervals.We see that the classier trained with the

SSS algorithm improves classication performance to about 75% for both datasets.

Model switching from Naive Bayes to TAN does not signicantly improve the per-

formance;apparently,the increase in the likelihood of the data does not cause a

decrease in the classication error.In both the NB and TAN cases,we see a per-

formance degradation as the unlabeled data are added to the smaller labeled dataset

(TAN-L and NB-L compared to TAN-LUL and NB-LUL).An interesting fact arises

from learning the same classiers with all the data being labeled (i.e.,the original

database without removal of any labels).Now,SSS achieves about 83% accuracy,

compared to the 75%achieved with the unlabeled data.Had we had more unlabeled

data,it might have been possible to achieve similar performance as with the fully

labeled database.This result points to the fact that labeled data are more valuable

than unlabeled data (see [4] for a detailed analysis).

26 Roberto Valenti,Nicu Sebe,Theo Gevers,and Ira Cohen

6 Conclusion

In this work we presented a complete system that aimes at human-computer inter-

action applications.We considered several instances of Bayesian networks and we

showed that learning the structure of Bayesian networks classiers enables learning

good classiers with a small labeled set and a large unlabeled set.

Our discussion of semi-supervised learning for Bayesian networks suggests the

following path:when faced with the option of learning Bayesian networks with la-

beled and unlabeled data,start with Naive Bayes and TANclassiers,learn with only

labeled data and test whether the model is correct by learning with the unlabeled data.

If the result is not satisfactory,then SSS can be used to attempt to further improve

performance with enough computational resources.If none of the methods using the

unlabeled data improve performance over the supervised TAN (or Naive Bayes),ei-

ther discard the unlabeled data or try to label more data,using active learning for

example.

In closing,it is possible to view some of the components of this work indepen-

dently of each other.The theoretical results of Section 3 do not depend on the choice

of probabilistic classier and can be used as a guide to other classiers.Structure

learning of Bayesian networks is not a topic motivated solely by the use of unlabeled

data.The three applications we considered could be solved using classiers other

than Bayesian networks.However,this work should be viewed as a combination of

all three components;(1) the theory showing the limitations of unlabeled data is used

to motivate (2) the design of algorithms to search for better performing structures of

Bayesian networks and nally,(3) the successful applications to an human-computer

interaction problem we are interested in solving by learning with labeled and unla-

beled data.

Acknowledgments

We would like to thank Marcelo Cirelo,Fabio Cozman,Ashutosh Garg,and Thomas

Huang for their suggestions,discussions,and critical comments.This work was sup-

ported by the Muscle NoE and MIAUCE European projects.

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